Image restoration results are presented using a new iterative/recursive method for removing a linear, spatially-invariant blur from an image. The new technique is a modification of the van Cittert iterative deconvolution method. Iterative deconvolution begins by guessing what the true image might be. If this guess is correct, then blurring it with the point spread function (PSF) will produce the observed image. If the guess is wrong, it can be corrected by the difference between the observed image and the blurred guess. The iterative method is very sensitive to noise in the image or error in the PSF, and convergence is very slow. Our modifications improve the speed of convergence and decrease noise sensitivity by using recursive restoration of higher-order image derivatives to guide restoration of lower order derivatives. The larger spatial extent of higher-order derivative kernels regularizes the procedure by smoothing out small-scale noise. Like the van Cittert iteration, the new iterative/recursive algorithm is linear and flux-conserving. We have used the new algorithm to restore both simulated Hubble Space Telescope (HST) images generated with PSFs computed with the Tiny Tim software and HST Planetary Camera images of the globular cluster NGC 6352. To account for the spatially varying PSF of the HST images, we divided each image into subsections over which the PSF is approximately constant and restored each section separately using a PSF appropriate for the center of the section. The simulations demonstrate that the intensity of point sources in the restored images is conserved to within a factor of 1-2 percent over a magnitude range of 6 dex. The color-magnitude diagram of NGC 6352 illustrates the level of photometric accuracy which can be obtained from images deconvolved using our technique with the PSFs currently available from the Space Telescope Science Institute. If better PSFs become available, we believe the color-magnitude diagram could improve significantly. For comparison, we have analyzed the unrestored images with PSF-fitting photometry.